"Choose wisely" - choose your tribe

Basics

As you certainly know, every tribe has some bonuses and a unique restricted technology tree. Every tribe will have to renounce on some technologies and make the best of what it has. It is very important that you choose your tribe carefully before you start. Take a look at my tribes page to see all differences.

Map type

The main distinction arises between land and sea maps. Three tribes (Babylonian, Hittite, Shang) cannot get Triremes and therefore should not be chosen when playing a high seas combat. Usually you will want to be able to get Juggernaughts at the Iron Age and other bonuses for your ships as well.
The best tribes at sea are the Greek, Minoan, Persian, Phoenician and Yamato tribes.The Hittite have also a bonus on their War ships but they cannot even get Triremes and therefore should only be chosen on very small maps or if you are not allowed to achieve the Iron Age.

When playing a land only map, you will want to get many bonuses for your land troops and also something that allows you to get troops more quickly than other tribes. Siege Weapons such as Catapults are a must because you can more easily defend a city with towers and walls on land maps. Academy and Cavalry units should not be missing either.
There are so many tribes that are strong at land maps that this choice depends on other circumstances as well.

Map size

On a small map, you should look for tribes that have bonuses that apply at the Tool or Bronze Age. For instance, the Phoenician tribe gets all its bonuses at the Iron Age and should not be chosen.
The best tribes at small maps and for rushes are the Assyrian, Hittite, Minoan, Shang and Sumerian tribes.
With the two latters ones, you can even try a "villager rush" since you get cheaper or tougher villagers and thus have a huge advantage if you find your opponent very early.

Preferences

What kind of player are you? Do you often forget switching between combat and production? If so, you should choose a tribe with all farm production bonuses (i. e. the plow and irrigation) and Elephants. If do not have to rebuild your farms as often, you can concentrate on other aspects of the game. Elephants are very tough and do not require much control in combat since they are very slow, too. Elephant Archers are better than Horse Archers in newbie hands; however, a good player can use the higher speed of the Horse Archer to gain an advantage.
It is not dumb to choose a tribe that has your favorite units. This usually means that you can maximize their use.

Strategy

This is the crucial difference between Warcraft and Age of Empires: in Age of Empires, you should plan ahead what you are doing and choose your tribe accordingly. Reactive strategies have the disadvantage that you may not have the units or bonuses you need to counter the enemy's strategy.
So you have to know

will you play offensively (rushes, early attacks) or defensively (walling in and towering)?

will you try to defeat all enemies, build a wonder or control all ruins or artifacts?

which tribe does your ally (if you have any) choose? Then you should choose a different tribe to get units that the other tribe does not have.

which type of unit plays the most important role in my strategy? For instance, when walling in, you will want good Archery units.

The Babylonian, Choson and Shang tribes have improved towers and/or walls.
The Shang are by far the best tribe in the early game, and also very good later on.

Team Games

The choice of the tribe is even more difficult when you are playing in a team. You should never choose the same tribe as your ally does, because this will allow your opponents to exploit their weaknesses. Try to choose a tribe in a matter that your tribes complement each other. On water maps, both tribes should have bonuses for their ships.

E. g. you are playing on a water map and your ally has chosen the Greek tribe. They have no good archers and no Elephants but otherwise nearly everything. You would like to choose the Phoenician tribe. They have a deadly +65% Catapult Trireme fire rate bonus, but they lack good Siege Weapons. This choice will make sure that you have a strong naval force, and the Greek player should share his Catapults with you (so you can defend yourself against naval attacks) while you deploy some of your Elephants and Chariot Archers at his base. By using the conversion trick where you temporarily declare war on your ally and convert his units, you cannot only break the 50 units limit more easily but actually get the control of your ally's units.

The particular choice depends much on your preferences and favorite
tactics. For instance, your ally could choose a tribe with defense bonuses while you attack early on, or both players choose a tribe that allows rushing etc. Because there are so many combinations possible, there is no
"perfect choice". That makes the game so enjoyable!

Conclusion

As you can see, there is no tribe that is dominating in all disciplines. Do not choose a tribe that has a particular weakness on the map type you are playing; and be aware that each tribe requires different tactics. So choosing a different tribe will result in a wholly different game - and this makes AoE interesting.